Yes, that is a service part, both the posi case and the ring & pinion gears.
The 812 cases were the LAST version, which was used during VERY LATE 61-64 production (VERY LATE 61-62 Vettes and -64 pass cars). Since there are no pictures, I can't tell if it has a posi or non-posi differential. The gears are 4.11------------------not a big demand for those anymore. If it does not have a posi unit, then the ONLY thing of significant value is the P case-------------------and that's not worth a whole lot since it was made AFTER regular production as a service part. For just a posi case, it has a fair value, but for the person looking for a correct dated case, 64 was the last time it was used on a production car (62 for Vettes).
If the P case was sold over the counter as just a bare case, then there would NOT be any stamped code on the pass side.